Advances in Difference Equations · 2013 · 20 citations · 16 references
Natural SciencesPhysicsComputational Fluid DynamicsComputational MechanicsComputational PhysicsConvergence AnalysisFinite Difference MethodsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsRichardson IterationStability Of Finite Difference Schemes
Numerical solution for the regularized long wave equation is studied by a new conservative Crank-Nicolson finite difference scheme. By the Richardson extrapolation technique, the scheme has the accuracy of without refined mesh. Conservations of discrete mass and discrete energy are discussed, and existence of the numerical solution is proved by the Browder fixed point theorem. Convergence, unconditional stability as well as uniqueness of the solution are also derived using energy method. Numerical examples are carried out to verify the correction of the theory analysis. MSC:65M06, 65N30.
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